Write 3^2 x 3^-3 x 3^6 as a single exponent.
A.) 3^4
B.) 3^5
C.) 3^11
D.) 27^5 ***
To simplify the expression 3^2 x 3^-3 x 3^6, we can use the rule of exponents that states when multiplying two exponentials with the same base, you add the exponents.
In this case, we have 3^2 x 3^-3 x 3^6. Adding the exponents, we get: 2 + (-3) + 6.
2 + (-3) = -1
Therefore, the expression simplifies to: 3^-1 x 3^6.
Again using the rule of exponents, when dividing two exponentials with the same base, you subtract the exponents.
In this case, we have 3^-1 x 3^6. Subtracting the exponents, we get -1 - 6 = -7.
Therefore, the expression simplifies to: 3^-7.
Now, since 3 raised to a negative exponent is equivalent to 1 divided by 3 raised to the positive exponent, we can rewrite 3^-7 as 1/3^7.
Therefore, the expression is equal to 1/3^7.
And finally, 1/3^7 can be written as 3^(-7).
Hence, the expression 3^2 x 3^-3 x 3^6 can be simplified as 3^(-7).
Answer: D.) 27^5
try again
when the bases are the same, just add the exponents
try again
when the bases are the same, just add the exponents
3^2 x 3^2 = 9 x 9 = 81 = 3^4
... not 9^4